Schedule of talks:

See also the Arithmetic Geometry Seminar

Abstracts

(Cueto): A classical result due to Clebsch from the mid-nineteenth century confirms that every complex space sextic curve (given as an intersection of a quadric and a cubic surface in projective 3-space) has exactly 120 tritangent planes. In this talk we will show how to use combinatorial methods arising from tropical geometry to revisit this classical problem and perform the analogous count over the reals and extensions thereof. This is joint work with Yoav Len, Hannah Markwig and Yue Ren (arXiv:2512.24277 and arXiv:2605.19905).

(Nolan): Toric varieties and their stack-theoretic generalizations are common objects of study in algebraic geometry and mirror symmetry. It is well-known that toric varieties are classified by combinatorial objects known as "fans," and conventional wisdom tells us that toric stacks (whatever they are) should also be classified by more general "stacky fans." In 2011, Geraschenko and Satriano (henceforth GS) proposed a definition of stacky fans, giving a combinatorial construction of a large class of toric Artin stacks. Gillam and Molcho later observed that the GS construction is not essentially surjective, i.e. there exist objects which deserve to be called "toric stacks" but do not arise via the GS construction. Our goal in this talk is to introduce a new, more general notion of "stacky fan" and explain how to construct an equivalence between our 2-category of stacky fans and a suitable 2-category of toric stacks. (We will also include a brief review of stack theory for the uninitiated.)

(J. Kim): The moduli space of cubic surfaces with a marked line lies naturally between the moduli space of fully marked and unmarked cubic surfaces and comes equipped with a $W(D_5)$-action corresponding to the stabilizer of the marked line. Hodge theoretic compactifications of these moduli spaces have been extensively studied by many, including Allcock—Carlson—Toledo, Dolgachev—van Geemen—Kondo, and Casalaina-Martin—Grushevsky—Hulek. In previous work, by using KSBA wall crossing, we described many different birational models of this moduli space via KSBA stable pairs. In this talk, we will discuss recent results regarding the $W(D_5)$-invariant birational geometry of these KSBA moduli spaces and ongoing work on the log minimal model program for these KSBA moduli spaces with respect to their log canonical divisor.

(Chen): Differentials on Riemann surfaces correspond to translation surfaces with cone points, where the zero orders of differentials determine the cone angles of translation surfaces. Affine transformations act on translation surfaces and preserve the zero type. These perspectives make differentials and their moduli spaces extensively studied in many areas. In this talk, I’ll first introduce the background of differentials and their moduli spaces. Then I’ll explain several recent AI-assisted works relevant to moduli spaces of differentials, which include elementary number theory, automorphisms of Riemann surfaces, topology of hyperplane arrangements, and special generating functions. These AI works were not prompted by me, and they are not as fancy as the million-dollar problems. However, the related questions naturally arose in my research field, and I did think about them before the era of AI. Both parts of the talk should be accessible to a general audience.

(VandeBogert): Matrix Schubert varieties naturally generalize determinantal varieties by allowing one to impose rank conditions on specified submatrices. Knutson–Miller identify their equivariant K-polynomials, which record alternating sums of syzygy characters, with double Grothendieck polynomials. A recent conjecture of Price–Stelzer–Yong predicts stability in the Schur supports of these polynomials as the underlying permutations are enlarged. In this talk, I’ll discuss a stronger phenomenon for Grassmannian matrix Schubert varieties: the individual syzygy representations stabilize, with multiplicities and homological degrees unchanged, under a simple operation on Young diagrams called Durfee stabilization. I’ll explain how the geometry of their desingularizations allows us to prove this through vector bundle cohomology on flag varieties and determine the sharp stability range. This is based on joint work with Sasha Pevzner, Steven V Sam, and Linus Setiabrata.

(Dominguez): Given a 3-term perfect complex E over a variety X and a nonnegative integer r, we define a virtual cycle over the r-th degeneracy loci of E. This is done by modifying the complex E after pulling it back to certain blow ups of X. We apply this construction to complexes over the Picard variety and the Hilbert schemes of non-singular complex projective surfaces. We recover, reprove and strengthen some of the known results involving the reduced cycles and the virtual cycles of the Hilbert schemes related to the curve counting theory and Vafa-Witten theory, respectively. This talk is based on joint work with Amin Gholampour.

(Defant): For each finite Coxeter group W and each standard Coxeter element of W, we construct a regular triangulation of the W-permutahedron. Our proof relies on the theory of total linear stability for Dynkin quivers. We also explore several notable combinatorial properties of these triangulations that relate the Bruhat order, the noncrossing partition lattice, and Cambrian congruences. Each triangulation gives an explicit mechanism for relating two different presentations of the corresponding braid group (the standard Artin presentation and Bessis's dual presentation). This is joint work with Melissa Sherman-Bennett and Nathan Williams.

(Li): To some extent, a perfect obstruction theory in the sense of Behrend--Fantechi is the shadow of a quasi-smooth derived Deligne--Mumford stack, ​ while a cosection of a perfect obstruction theory in the sense of Kiem--Li is the shadow of a (-1)-shifted function on a quasi-smooth derived Deligne--Mumford stack. In this talk, we will introduce shifted logarithmic functions on derived stacks equipped with log structures of Deligne--Faltings type, and logarithmic cosections of perfect obstruction theories. As an application, we will present a decomposition theorem for virtual cycles, after Log GLSM. If time permits, we will discuss another facet of shifted logarithmic functions: their derived critical loci carry shifted logarithmic symplectic structures, building on the work of Calaque-Safronov.

(Ma): Foldings of ADE resolutions are quotients of the minimal resolutions of Kleinian singularities by Dynkin diagram symmetries. In this talk, I will describe a root-theoretic formula for the untwisted part of their orbifold quantum cohomology. The idea is to adapt the work of Bryan and Gholampour on quantum multiplication for ADE resolutions to the setting of foldings. I will then discuss several further questions concerning crepant resolutions of these foldings.

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Past Seminars

Ohio State University Algebraic Geometry Seminar-Year 2025-2026

Ohio State University Algebraic Geometry Seminar-Year 2024-2025

Ohio State University Algebraic Geometry Seminar-Year 2023-2024

Ohio State University Algebraic Geometry Seminar-Year 2022-2023

Ohio State University Algebraic Geometry Seminar-Year 2021-2022

Ohio State University Algebraic Geometry Seminar-Year 2020-2021

Ohio State University Algebraic Geometry Seminar-Year 2019-2020

Ohio State University Algebraic Geometry Seminar-Year 2018-2019

Ohio State University Algebraic Geometry Seminar-Year 2017-2018

Ohio State University Algebraic Geometry Seminar-Year 2016-2017

Ohio State University Algebraic Geometry Seminar-Year 2015-2016

Ohio State University Algebraic Geometry Seminar-Year 2014-2015

Ohio State University Algebraic Geometry Seminar-Year 2013-2014

This page is maintained by Angie Cueto and Dave Anderson.